An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
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Page ix
... involve 2i + 1 arbi- trary constants • 5. Derivation of successive harmonics from the zonal harmonic by differentiation 6. Tesseral and sectorial harmonics 7. Expression of tesseral and sectorial harmonics in a completely developed form ...
... involve 2i + 1 arbi- trary constants • 5. Derivation of successive harmonics from the zonal harmonic by differentiation 6. Tesseral and sectorial harmonics 7. Expression of tesseral and sectorial harmonics in a completely developed form ...
Page 3
Norman Macleod Ferrers. of p . The solid harmonics of this form will involve two of the variables , x and y , only in the form x2 + y2 , or will be functions of x2 + y2 and z . Harmonics independent of 4 are called Zonal Harmonics , and ...
Norman Macleod Ferrers. of p . The solid harmonics of this form will involve two of the variables , x and y , only in the form x2 + y2 , or will be functions of x2 + y2 and z . Harmonics independent of 4 are called Zonal Harmonics , and ...
Page 4
... spherical surface harmonics , P , will be the zonal surface harmonic of the K degree . When it is necessary to particularise the variable The spherical harmonic of the degree i will involve 2i+1 arbi- trary constants.
... spherical surface harmonics , P , will be the zonal surface harmonic of the K degree . When it is necessary to particularise the variable The spherical harmonic of the degree i will involve 2i+1 arbi- trary constants.
Page 5
... involve none but positive integral powers of μ . But P is a particular integral of the equation d αμ { ( 1 – M2 ) d.f ( u ) ) - ti ( +1 ) f ( u ) = 0 ...... ( 3 ) , dμ and the most general form of f ( u ) must involve two ar- bitrary ...
... involve none but positive integral powers of μ . But P is a particular integral of the equation d αμ { ( 1 – M2 ) d.f ( u ) ) - ti ( +1 ) f ( u ) = 0 ...... ( 3 ) , dμ and the most general form of f ( u ) must involve two ar- bitrary ...
Page 6
... equation ( 2 ) of the form of a rational integral function of u involves but one arbitrary constant , and that as a 6 ZONAL HARMONICS . Investigation of expression for P; in terms of u, by Lagrange's Tesseral and sectorial harmonics.
... equation ( 2 ) of the form of a rational integral function of u involves but one arbitrary constant , and that as a 6 ZONAL HARMONICS . Investigation of expression for P; in terms of u, by Lagrange's Tesseral and sectorial harmonics.
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Common terms and phrases
Assistant-Master axis b²+w become infinite bounding surface C₁ Cambridge centre Chap co-ordinates coefficients component attraction confocal ellipsoid corresponding cos² Crown 8vo degree denoted distance dV dV dy dz Edited by Rev ellipsoidal harmonics equal Eton College expression external point Extra fcap factor fcap Fellow of St follows Greek Hence homogeneous function internal John's College lamina late Fellow LATIN monics multiplying numerous obtain Oxford P₁ P₂ plane positive integer potential Professor radius rational integral function satisfies the equation series of zonal shewn sin² solid angle solid harmonic solutions sphere spherical harmonic spherical shell suppose surface harmonic Tesseral thickness Trinity College V₁ writing y+b² y+c² zonal harmonics αμ αμσ µ² µ³ µ³)³ προ
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